Shifted Popov Criterion

Abstract

In this paper, a new stability criterion for nonlinear feedback systems which include a nonlinearity consisting of the main term and the deviation term is presented. The main term is assumed to be time-invariant and to depend only upon the output of the linear part. The deviation term is allowed to be time-varying and to depend on all state variables. The criterion converges to the Popov criterion when the deviation term approaches 0. It generally gives a sharper result than the circle criterion. The result is especially useful to analyze stability of feedback systems, such as fuzzy control systems, which contain “slightly time-varying and/or multivariable” nonlinearities.